Question

A can complete a piece of work on 15 days and B can complete the same work in 12 days. If

both of them work together how long will they take to finish the work?​

Answer 1

Answer:

The time taken by A and B to finish the work together is nearly 20/3 days.

Step-by-step explanation:

Given :

• A can complete a piece of work on 15 days
• B can complete the same work in 12 days.

To find :

the number of days taken by them to finish the work together.

Solution :

Let's find out how much work will be completed by A and B alone in one day.

➙ A can complete a piece of work on 15 days.

In one day, work done by A = 1/15

➙ B can complete the same work in 12 days.

In one day, work done by B = 1/12

➙ Let's assume both A and B take x days to finish the work together.

In one day, work done by A and B together = 1/x

So,

Work done by A and B together in one day = Work done by A alone in one day + Work done by B alone in one day

   $\sf \dfrac{1}{x}=\dfrac{1}{15}+\dfrac{1}{12} \\\\ \sf \dfrac{1}{x}=\bigg(\dfrac{1}{15} \times \dfrac{4}{4} \bigg)+ \bigg(\dfrac{1}{12} \times \dfrac{5}{5} \bigg) \\\\ \sf \dfrac{1}{x}=\dfrac{4}{60}+\dfrac{5}{60} \\\\ \sf \dfrac{1}{x}=\dfrac{4+5}{60} \\\\ \sf \dfrac{1}{x}=\dfrac{9}{60} \\\\ \sf \dfrac{1}{x}=\dfrac{3}{20} \\\\ \sf x=\dfrac{20}{3}$

 x ≈ 6.67

Therefore, The time taken by A and B to finish the work together is nearly 6.67 days.

Answer 2

$\sf{Answer}$

Step-by-step-explanation

Given:-

• A can complete work on 15 days
• B can complete work on 12 days

To find :-

• Work done by A& B together

Solution:-

First we will find one day work of them

Work done by A = 15days

One day work of A = $\sf\dfrac{1}{15}$

Work done By B = 12 days

One day work done by B = $\sf\dfrac{1}{12}$

Work done by A&B together in day = one day work of A + one day Work of B

So , work done by A&B together

= $\sf\dfrac{1}{15}$+$\sf\dfrac{1}{12}$

= $\sf\dfrac{4+5}{60}$

= $\sf\dfrac{9}{60}$

= $\sf\dfrac{3}{20}$

So, Work done by A&B together in one day = $\sf\dfrac{3}{20}$

___________________

So, total work done by A&B together = $\sf\dfrac{20}{3}$

So, total work done by A&B together =$\sf\dfrac{20}{3}$= 6.67 days